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Item Comparing network models of gap gene interaction during Drosophila melanogaster development(Montana State University - Bozeman, College of Letters & Science, 2021) Andreas, Elizabeth Anne; Chairperson, Graduate Committee: Tomas GedeonEarly development of Drosophila melanogaster (fruit fly) facilitated by the gap gene network has been shown to be incredibly robust, and the same patterns emerge even when the process is seriously disrupted. In this thesis we plan to investigate this robustness using a previously developed computational framework called Dynamic Signatures Generated by Regulatory Networks (DSGRN). The principal result of this research has been in extending DSGRN to study how tissue-scale behavior arises from network behavior in individual cells, such as gap gene expression along the anterior-posterior (A-P) axis of the Drosophila embryo. Essentially, we extend DSGRN to study cellular systems where each cell contains the same network structure but operates under a parameter regime that changes continuously from cell to cell. We then use this extension to study the robustness of two different models of the gap gene network by looking at the number of paths in each network that can produce the observed gap gene expression. While we found that both networks are capable or replicating the data, we hypothesize that one network is a better fit than the other. This is significant in two ways; finding paths shows us that the spatial data can be replicated using a single network with different parameters along the A-P axis, and that we may be able to use this extension of DSGRN to rank network models.Item Visual sample plan and prior information: what do we need to know to find UXO?(Montana State University - Bozeman, College of Letters & Science, 2016) Flagg, Kenneth A.; Writing Project Advisor: Megan HiggsMilitary training and weapons testing activities leave behind munitions debris, including both inert fragments and explosives that failed to detonate. The latter are known as unexploded ordnance (UXO). It is important to find and dispose of UXO items that are located where people could come into contact with them and cause them to detonate. Typically there exists uncertainty about the locations of UXO items and the sizes of UXO- containing regions at a site, so statistical analyses are used to support decisions made while planning a site remediation project. The Visual Sample Plan software (VSP), published by the Pacific Northwest National Laboratory, is widely used by United States military contractors to guide sampling plan design and to identify regions that are likely to contain UXO. VSP has many features used for a variety of situations in UXO cleanup and other types of projects. This study focuses on the sampling plan and geostatistical mapping features used to find target areas where UXO may be present. The software produces transect sampling plans based on prior information entered by the user. After the sample data are collected, VSP estimates spatial point density using circular search windows and then uses Kriging to produce a continuous map of point density across the site. I reviewed the software's documentation and examined its output files to provide insight about how VSP does its computations, allowing the software's analyses to be closely reproduced and therefore better understood by users. I perform a simulation study to investigate the performance of VSP for identifying target areas at terrestrial munitions testing sites. I simulate three hypothetical sites, differing in the size and number of munitions use areas, and in the complexity of the background noise. Many realizations of each site are analyzed using methods similar to those employed by VSP to delineate regions of concentrated munitions use. I use the simulations to conduct two experiments, the first of which explores the sensitivity of the results to different search window sizes. I analyze two hundred realizations of the simplest site using the same sampling plan and five different window sizes. Based on the results, I select 90% of the minor axis of the target area of interest as the window diameter for the second experiment. The second experiment studies the effects of the prior information about the target area size and spatial point density of munitions items. For each site, I use four prior estimates of target area size and three estimates of point density to produce twelve sampling plans. One hundred realizations of each site are analyzed with each of the twelve sampling plans. I evaluate the analysis in terms of the detection rates of munitions items and target areas, the distances between undetected munitions items and identified areas, the total area identified, and other practical measures of the accuracy and efficiency of the cleanup effort. I conclude that the most accurate identification of target areas occurs when the sampling plan is based on the true size of the smallest target area present. The prior knowledge of the spatial point density has relatively little impact on the outcome.Item Is model averaging the solution for addressing model uncertainty? : methodological insights, tools for assessment, and considerations for practical use(Montana State University - Bozeman, College of Letters & Science, 2016) Banner, Katharine Michelle; Chairperson, Graduate Committee: Steve Cherry; Megan Higgs (co-chair); Megan Higgs was a co-author of the article, 'Considerations for assessing model averaging of regression coefficients' in the journal 'Ecological applications' which is contained within this thesis.; Megan Higgs was a co-author of the article, 'Investigating the posterior variance of partial regression coefficients resulting from three common methods for multimodel inference' submitted to the journal 'Annals of applied statistics' which is contained within this thesis.; Megan Higgs was a co-author of the article, 'The model averaged posteriors plot MAPP package for R statistical software' submitted to the journal 'Journal of statistical software' which is contained within this thesis.Model averaging (MA) was developed as a way to combine predictions from many models, with the goal of reducing bias and incorporating model uncertainty into final predictive inferences. A new flavor of MA, focused on averaging partial regression coefficients over multiple models, has gained traction in fields such as Ecology, Biology, and Political Science, with motivation stemming from the concern that inferences based on a single model are too 'naive' (i.e., do not fairly reflect sources of substantial uncertainty). However, coefficients appearing in multiple models do not necessarily hold the same interpretation across models, and averaging over them has the potential to result in inferences that are difficult to interpret. A gap exists between the theoretical development of MA and its current use in practice, potentially leaving well-intentioned researchers with unclear inferences, or difficulties justifying decisions to use (or not use) MA. Furthermore, it is questionable whether the perceived benefit of accounting for an additional source of uncertainty is realized in terms of increased variance for quantities of interest. In this work, we revisit relevant foundations of regression modeling, suggest more explicit notation and graphical tools, and discuss how individual model results are combined to obtain a MA result, with the goal of helping researchers make informed decisions about MA. We present a new package for R Statistical Software providing plotting functions for visualizing components going into the MA posterior distribution. This package is meant to be used to assess the implicit assumptions made by using MA for regression coefficients, complete with guidelines for use and examples. We also design and conduct a simulation study to investigate how the variance for a partial regression coefficient of interest is different for three different approaches used within multimodel inference (MA using all models, MA using a subset of models, and conditioning inferences on one model). We assess whether the perceived benefit of accounting for model uncertainty is actually realized when more models are used for final inference, with the goal of helping researches weigh tradeoffs between using variants of MA in place of one well thought out model.